Field · Emerged 1915 – 1974

Compact Objects

What is left when a star dies, and how dense can matter become?

5 chapters4 min read7 turning points 1 open problem

Branched from: Stellar Astrophysics + General Relativity
Branched into: Not yet surveyed past here
Figures: Walter Adams, Arthur Eddington, Subrahmanyan Chandrasekhar, Walter Baade, Fritz Zwicky, J. Robert Oppenheimer, Jocelyn Bell Burnell, Antony Hewish, Louise Webster, Paul Murdin, Tom Bolton, Russell Hulse, Joseph Taylor

In brief

When a star exhausts its fuel, gravity wins. What remains depends on its mass. Stars like the Sun end as white dwarfs, Earth-sized embers held up by the quantum resistance of electrons to being squeezed. Heavier stars explode as supernovae and leave neutron stars, a city-sized ball of neutrons as dense as an atomic nucleus. The heaviest collapse into black holes, from which not even light escapes.

Each of these was first a theoretical deduction, often resisted. Eddington ridiculed Chandrasekhar's mass limit, neutron stars were proposed in 1934 and dismissed for decades, and black holes were long considered a mathematical curiosity of general relativity. Between 1967 and 1974, pulsars, X-ray binaries and a binary pulsar made all three real.

Key ideas

Degeneracy pressureEnters 1930 – 1935: Electrons, and neutrons, cannot share quantum states, so squeezing them together forces them into higher-energy states. The resulting pressure holds up white dwarfs and neutron stars without any heat.
Chandrasekhar limitEnters 1930 – 1935: About 1.4 times the Sun's mass: the largest mass electron degeneracy can support. A heavier stellar core must collapse further.
Neutron starEnters 1934: The collapsed core of a massive star, about 1.4 solar masses in a sphere around 12 km in radius. A teaspoonful would weigh billions of tonnes.
PulsarEnters 1967 – 1968: A spinning, magnetised neutron star whose beams of radio waves sweep past Earth like a lighthouse, producing extraordinarily regular pulses.
Black holeEnters 1939: A region where gravity is so strong that nothing, not even light, can escape from inside its boundary, the event horizon. For the Sun's mass, the horizon would have a radius of about 3 km.

Chapter I

Absurdly Dense

Sirius, the brightest star in the night sky, wobbles as it moves, and in 1862 a faint companion, Sirius B, was seen. In 1915 Walter Adams measured its spectrum. It was white-hot, yet so faint that it had to be tiny, and modern measurements put it at about the size of the Earth, while its orbit showed it had about the Sun's mass. A cubic centimetre of it weighs about two tonnes. Astronomers at first dismissed such a density as nonsense, as Eddington later recalled, but in 1926 Ralph Fowler showed that the new quantum statistics of statistical mechanics allowed it. Electrons packed that tightly resist further squeezing, whatever the temperature, and that pressure holds up white dwarfs.

Chapter II

The Limit

In 1930, on the ship from India to England, Subrahmanyan Chandrasekhar, aged nineteen, added special relativity to Fowler's theory. The electrons in a heavy white dwarf move close to the speed of light and become easier to compress, so above a certain mass, about 1.4 times the Sun's, nothing can stop the collapse. At a meeting of the Royal Astronomical Society in 1935, Eddington, the most famous astronomer of the age, ridiculed the result immediately after Chandrasekhar presented it, and the audience laughed. Chandrasekhar left Britain for Chicago and moved on to other problems. He received the Nobel prize in 1983.

What happened above the limit? In 1934 Walter Baade and Fritz Zwicky proposed that supernovae are the collapse of stars into neutron stars. In 1939 J. Robert Oppenheimer and his students showed that neutron stars also have a maximum mass, and that a heavier core collapses without end, sealing itself off from the universe. The Second World War took Oppenheimer to Los Alamos, and the subject slept.

Chapter III

Pulsars and Black Holes

In 1967 Jocelyn Bell, a PhD student in Antony Hewish's group at Cambridge, spotted a regular pulse in a radio survey, one pulse every 1.337 seconds. Within a year, faster pulsars were found in the Vela and Crab supernova remnants, and only a spinning neutron star could flash so quickly and so regularly. Neutron stars were real. The Crab pulsar sits at the centre of the Crab Nebula, the remains of a supernova recorded by Chinese astronomers in 1054.

Black holes followed. In 1971–72 Louise Webster, Paul Murdin and Tom Bolton showed that the X-ray source Cygnus X-1 is an invisible object too heavy to be a neutron star. And in 1974 Russell Hulse and Joseph Taylor found two neutron stars orbiting each other, whose orbit shrank exactly as general relativity predicts from the emission of gravitational waves.

Chapter IV

A Closer Look: A Teaspoon of Star

Density is mass divided by volume, $\rho = M / \tfrac43 \pi R^3$ . The Sun's mass is $2 \times 10^{30}$ kg.

A white dwarf of 0.6 solar masses and radius 6,000 km, about the size of the Earth, has density

\rho = \frac{0.6 \times 2 \times 10^{30}}{\tfrac43 \pi (6 \times 10^6)^3} \approx 1.3 \times 10^9 \text{ kg/m}^3 .

A teaspoon, 5 millilitres, would weigh about 6.6 tonnes, as much as an elephant.

A neutron star of 1.4 solar masses and radius 12 km gives

\rho = \frac{1.4 \times 2 \times 10^{30}}{\tfrac43 \pi (1.2 \times 10^4)^3} \approx 3.9 \times 10^{17} \text{ kg/m}^3 .

A teaspoon weighs about $2 \times 10^{12}$ kg, two billion tonnes, roughly the mass of a small mountain. That is the density of an atomic nucleus: a neutron star is in effect a single nucleus the size of a city.

A black hole has no surface, but its horizon has a size, the Schwarzschild radius $r_s = 2GM/c^2$ . For one solar mass,

r_s = \frac{2 \times 6.67 \times 10^{-11} \times 2 \times 10^{30}}{(3.0 \times 10^8)^2} \approx 3 \text{ km} .

A neutron star of 1.4 solar masses has a Schwarzschild radius of about 4 km, so its 12 km radius is only about three times that. This is why general relativity is essential for describing it.

Neutron stars also spin astonishingly fast, because a collapsing star keeps its angular momentum as it shrinks, as a skater spins faster pulling in their arms. The fastest known pulsar spins 716 times a second. At its equator, 12 km from the axis, the surface moves at

2\pi \times 12 \text{ km} \times 716 \approx 54{,}000 \text{ km/s} ,

about 18% of the speed of light.

Chapter V

Laboratories of Extremes

Compact objects are now studied with every kind of telescope and with gravitational-wave detectors. The 2017 merger of two neutron stars was seen in gravitational waves and in light, and forged heavy elements such as gold. Black holes of millions of solar masses sit at the centres of galaxies, including our own, the subject of galactic astronomy. What matter is like inside a neutron star, the densest matter in the universe short of a black hole, is still unknown.

Turning points7

1915DISCOVERY
A star as dense as nothing on Earth
Walter Adams measures the spectrum of Sirius B, the faint companion of Sirius. It is hot and white, yet dim, so it must be tiny: about the Sun's mass in a body the size of the Earth. Astronomers at first dismissed the implied density as nonsense, as Eddington later recalled. In 1926 Ralph Fowler showed that electron degeneracy pressure, from the new quantum statistics, could support it.
Walter Adams
› Sources (1)
- Adams, W. S. (1915). The spectrum of the companion of Sirius. Publications of the Astronomical Society of the Pacific 27: 236–237.
1930 – 1935DISCOVERYContested
The Chandrasekhar limit
On the voyage from India to Cambridge, nineteen-year-old Subrahmanyan Chandrasekhar combines relativity with degeneracy pressure and finds that white dwarfs cannot exceed a certain mass. Anything heavier must collapse. At a meeting of the Royal Astronomical Society in 1935, Eddington publicly ridiculed the idea. Chandrasekhar received the Nobel prize for his work on stellar structure in 1983.
What is disputed
Wilhelm Anderson (1929) and Edmund Stoner (1930) had found related limits using less complete treatments, and some historians argue their priority is underplayed. The bigger dispute was Eddington's opposition, which delayed acceptance for years. Most astronomers deferred to Eddington at the time, and the limit was not widely accepted until the late 1930s.
Arthur Eddington, Subrahmanyan Chandrasekhar
› Sources (2)
- Chandrasekhar, S. (1931). The maximum mass of ideal white dwarfs. Astrophysical Journal 74: 81–82.
- Miller, A. I. (2005). Empire of the Stars: Obsession, Friendship, and Betrayal in the Quest for Black Holes. Houghton Mifflin.
1934DISCOVERY
Supernovae and neutron stars
Two years after the neutron was discovered, Walter Baade and Fritz Zwicky propose that a supernova is the collapse of an ordinary star into a "neutron star", releasing enormous energy, and that supernovae produce cosmic rays. The idea was far ahead of the evidence and was largely ignored for three decades.
Walter Baade, Fritz Zwicky
› Sources (1)
- Baade, W. & Zwicky, F. (1934). On super-novae. Proceedings of the National Academy of Sciences 20(5): 254–259.
1939DISCOVERY
Neutron star limits and gravitational collapse
J. Robert Oppenheimer and George Volkoff calculate that neutron stars also have a maximum mass. With Hartland Snyder, Oppenheimer then shows that a star heavier than that collapses without limit, cutting itself off from the outside universe. The paper describes what John Wheeler later named a black hole. War intervened, and the work was neglected for twenty years.
J. Robert Oppenheimer
› Sources (2)
- Oppenheimer, J. R. & Volkoff, G. M. (1939). On massive neutron cores. Physical Review 55(4): 374–381.
- Oppenheimer, J. R. & Snyder, H. (1939). On continued gravitational contraction. Physical Review 56(5): 455–459.
1967 – 1968EXPERIMENTContested
Pulsars
Jocelyn Bell, a Cambridge graduate student checking chart recordings from a radio telescope she helped build, notices "a bit of scruff": pulses every 1.337 seconds, regular as a clock. The team half-seriously labelled it LGM-1, for "little green men". Pulsars were soon identified as spinning neutron stars, the first proof that neutron stars exist.
What is disputed
The 1974 Nobel prize went to her supervisor Antony Hewish and to Martin Ryle, not to Bell. Fred Hoyle and others protested at the time. Bell Burnell has said she does not resent it, as supervisors then took responsibility for student work. In 2018 she received a Breakthrough Prize and gave the $3 million to fund physics studentships for under-represented groups.
Jocelyn Bell Burnell, Antony Hewish
› Sources (1)
- Hewish, A., Bell, S. J., Pilkington, J. D. H., Scott, P. F. & Collins, R. A. (1968). Observation of a rapidly pulsating radio source. Nature 217: 709–713.
1971 – 1972EXPERIMENT
The first black hole
The X-ray source Cygnus X-1 is found to orbit a massive blue star. Louise Webster and Paul Murdin in Britain, and Tom Bolton in Canada, measure the orbit and find that the unseen companion is too heavy to be a neutron star. It became the first widely accepted black hole. Stephen Hawking bet Kip Thorne in 1974 that it was not one, and conceded in 1990.
Louise Webster, Paul Murdin, Tom Bolton
› Sources (2)
- Webster, B. L. & Murdin, P. (1972). Cygnus X-1 — a spectroscopic binary with a heavy companion? Nature 235: 37–38.
- Bolton, C. T. (1972). Identification of Cygnus X-1 with HDE 226868. Nature 235: 271–273.
1974EXPERIMENT
The binary pulsar
Russell Hulse and Joseph Taylor discover a pulsar in a tight orbit with another neutron star. Timing its pulses over years, Taylor and colleagues show the orbit shrinking at exactly the rate general relativity predicts for energy lost to gravitational waves. It was the first evidence that gravitational waves exist, and won the 1993 Nobel prize.
Russell Hulse, Joseph Taylor
› Sources (2)
- Hulse, R. A. & Taylor, J. H. (1975). Discovery of a pulsar in a binary system. Astrophysical Journal 195: L51–L53.
- Taylor, J. H. & Weisberg, J. M. (1982). A new test of general relativity: gravitational radiation and the binary pulsar PSR 1913+16. Astrophysical Journal 253: 908–920.

Applications

Where it is used

Gravitational waves
A galaxy-sized detector
Pulsars are such precise clocks that a network of them spread across the galaxy can register gravitational waves light-years long, which stretch and squeeze the space the pulses cross. In 2023 pulsar timing arrays reported evidence for a background of such waves, probably from pairs of supermassive black holes.
› Sources (1)
- Agazie, G. et al. (NANOGrav) (2023). The NANOGrav 15 yr data set: evidence for a gravitational-wave background. Astrophysical Journal Letters 951(1): L8.
Navigation
Pulsars as a galactic GPS
Because each pulsar has a known, stable rhythm, a spacecraft timing X-ray pulses from several of them can work out its own position. NASA demonstrated it in 2017 on the International Space Station, locating the station to within about 16 km, and often within 5 km.
› Sources (1)
- Mitchell, J. W. et al. (2018). SEXTANT X-ray pulsar navigation demonstration: initial on-orbit results. Proceedings of the AAS Guidance and Control Conference, AAS 18-155.

Open problems

Where the map runs out

Open

What is inside a neutron star?

Open as of 2026. X-ray and gravitational-wave measurements are narrowing the range.

The core of a neutron star is denser than an atomic nucleus. Is it made of neutrons, of more exotic particles, or of free quarks? The answer determines how large a neutron star is for its mass, and the heaviest one that can exist.

Why it is hard: Matter at these densities cannot be made in any laboratory, and the strong force is too complicated to calculate there from first principles. Astronomers must infer the interior from masses and radii of distant stars, measured with X-ray timing and from the deformation of neutron stars in mergers.
What resolving it unlocks: The behaviour of matter at the highest densities in the universe, and the dividing line between neutron stars and black holes.

› Sources (1)

Özel, F. & Freire, P. (2016). Masses, radii, and the equation of state of neutron stars. Annual Review of Astronomy and Astrophysics 54: 401–440.